MAP 1 Physics of Motion Lecture Notes PDF

Lecture The Physics of Motion Module Medical Applications of Physics Code MAP.1 Lecturer Prof. Kevin McGuigan  Learning Outcomes Define: time, displacement and distance, velocity and speed, MAP.01.01 acceleration. MAP.01.02 Differentiate between vectors a...

Lecture The Physics of Motion Module Medical Applications of Physics Code MAP.1 Lecturer Prof. Kevin McGuigan  Learning Outcomes Define: time, displacement and distance, velocity and speed, MAP.01.01 acceleration. MAP.01.02 Differentiate between vectors and scalars. MAP.01.03 Explain Newton’s Laws of Straight-Line Motion. MAP.01.04 Differentiate between mass, inertia and momentum. Describe the role of external forces in effective weight and g- MAP.01.05 force. MAP.01.06 Define work, power and energy. MAP.01.07 Differentiate between kinetic energy and potential energy. Differentiate between the conservation of energy and the MAP.01.08 Work-Energy Principle. Section 1 Basic quantities/entities In mechanics, several characters play leading roles These are: time (t) displacement (s) velocity (v) acceleration (a) Time (t) is “the indefinite continued progress of existence and events in the past, present, and future regarded as a whole” (OED) and is measured in units of seconds In SI system 1 second = duration of 9,192,631,770 periods of the radiation transition between two hyperfine levels of the Cs133 ground state! Or 1/86400 of the mean solar day. Displacement (s) is distance measured in a given direction and is measured in metres (m). Displacement is a vector quantity. Distance is a scalar quantity. Meter (m) Was originally intended to be one ten-millionth (1/10,000,000) of the distance from the Earth′s equator to the North Pole (at sea level). Earth’s polar circumference = 40,007 km Earth’s equatorial circumference = 40,075 km Since 1983, it has been defined as "the length of the path travelled by light in vacuum during a time interval of 1⁄299,792,458 of a second.“ (speed of light in a vacuum = 299,792,458 m/s) Velocity (v) is ∆𝑠 rate of change of 𝑣= displacement. ∆𝑡 v is measured in units of metres per second (ms ). -1  Acceleration (a) is the rate of change of velocity. ∆𝑣 𝑎= ∆𝑡 Acc. is measured in units of metres per second per second (ms ). -2 Deceleration occurs when the velocity reduces (a is negative). The acceleration that we are most familiar with is that due to gravity (g). g = 9.81ms-2. Since g is a constant (slight variations with altitude), all objects fall at the same rate, regardless of their mass. Section 2 Straight-line Motion We can exactly describe or determine all types of straight line motion using Newton’s Three Laws of Rectilinear Motion (not to be confused with Newton’s First, Second & Third Laws). If: u = initial velocity (ms ) -1 v = final velocity (ms ) -1 s = displacement (m) a = acceleration (ms-2) t = time (s) Newton’s Three Laws of Rectilinear Motion v = u + at v = u +2as 2 2 s = ut + ½at 2 Physics Prof. falls 15m from a ladder while performing a demonstration. 1. Calculate their impact velocity? 2. Calculate the duration of their fall? What is known and what is unknown? u = 0 ms-1 v = ? ms-1 a = g = 9.81 ms-2 ~ 10 ms-2 s = 15 m t=?s Calculate their impact velocity? Find an equation containing v with only 1 unknown variable. v = u + at v = u +2as 2 2 s = ut + ½at 2 Vel ~ 62 kph ~ 40 mph Calculate the duration of their fall? v = u + at v = u +2as 2 2 s = ut + ½at 2 Or Section 3 Forces Newton’s First Law: “All objects tend to remain at rest or in uniform straight line motion (at constant velocity) unless acted upon by an external force.” An object will only change velocity (magnitude or direction) if (& only if) a force is exerted upon it. Gravitational Electrostatic (Coulombic) Forces come in many different forms.  But what is a force? Newton’s Second Law F = m.a “A force is any action that alters, or tends (tries) to alter, a body’s state of rest or of uniform motion in a straight line”.  Force has units of Newtons (N) where: 1N = force that provides 1kg with an acceleration of 1ms-2. The tendency to remain in an initial velocity state is called Inertia. The bigger the mass the larger the resistance to change. Inertia has identical units to mass (kg) The force that we would be most familiar with is WEIGHT (W). Usually W = mg We can sometimes increase the “apparent” weight of an object by subjecting it to additional forces. This increase in Effective Weight (Weff) can be seen whenever we ascend in an elevator. Weff = m(g + a)  Weff = m(g + a) Weight is defined as a reaction force (opposite to the acceleration due to gravity) directed perpendicularly upwards from the surface Effective weight changes whenever external forces are acting upon a body. Fighter pilots are routinely subjected to 9g accelerations during combat manoeuvres. Group Captain Sir Douglas Bader Lost both legs in an crash in 1931. In WWII he was credited with 20 aerial victories. He recovered more quickly from g-force induced blackouts than most other pilots since he had no legs for the blood to pool into during high “g” manoeuvres.  Ejection seats create up to 25g often producing spinal injury even when executed correctly. Washing machines creates up to 200g for 1100rpm spin cycle - fatal for toddlers Peregrine falcon (Falco peregrinus) can dive at their prey at >320kph and are subjected to accelerations >20 g as they pull out of their dives. Effective weight can be less than gravitational weight under right conditions. See https://www.youtube.com/watch?v=u9pkjHWAZLs Explains why people feel faint if they get up from a reclining position too quickly, especially if they have been asleep. Upwards acceleration causes blood to have a higher effective weight, which is harder for the heart to pump to the brain. Section 4 Work & Energy Work Work is done when a force F moves a body through a distance d along the direction of F. W = F.d (unit = joule (J) Energy Capacity or ability to do work (unit = joule) Energy = Work = F.d 1 J = Energy needed to exert a force of 1N over a distance of 1m There are many types of energy: 1. Chemical 2. Thermal 3. Nuclear/atomic 4. Acoustic 5. Mechanical Mechanical Energy comes in 2 forms Kinetic Energy (resulting from movement) Potential Energy (resulting from electrical charge, internal stress, but usually relative position) PE = mgh h = height above agreed reference pt.  PE to KE Conservation of Energy Energy can't be created or destroyed, just transformed from one form to another. PE to KE to PE to KE to….. Work-Energy Principle Or Work = DKE